Calculating-instrument for percentage and proportion



(N0 ModeL) M. T. FREEMAN.

CALCULATING INSTRUMENT FOR PERCENTAGE AND PROPORTION.

No; 319,808. Patented June 9, 1885.

Wm -%EEEL EM N. PETERS. PholuLlihogmphar, Washingicm D (L UNITED STATES PATENT Orrrca.

METHVEN T. FREEMAN, OF RICHMOND, VIRGINIA.

CALCULATING-INSTRUMENT FOR PERCENTAGE AND PROPORTION.

SPECIFICATION forming part of Letters Patent No. 319,808, dated June 9, 1885.

Application filed August 4, 1894. (No model.)

T0 at whom it may concern:

Be it known that I, METHVEN T. FREEMAN, of Richmond, in the county of Henrico and State of Virginia, have invented certain new and useful Improvements in Calculators for Percentage and Proportion; and I do hereby declare that the following is' a full, clear, and exact description of the invention, which will enable others skilled in the art to which it appertains to make and use the same, reference being had to the accompanying drawings, and to the letters of reference marked thereon, which form part of this specification.

The object of my invention is to facilitate the solution of such problems as the following, among many that may be solved readily by means of it: (a) to reduce any two or more numbers to a regular percentage; (1)) to reduce any two or more given numbers to a percentage when one of the numbers is allowed a greater per cent. than its pro rata proportion really amounts to, without first reducing the remaining numbers to a percentage to be ap plied to the remaining part of the one hundred per cent. (c) to divide a given number on fixed percentage; (d) to divide a given number into parts, so that the said parts shall stand to one another in the same ratio that any several named numbers shall stand to one another, without first reducing these named numbers to percentages; (c) to ascertain the circumference of a circle, the diameter being known, or, vice versa, to determine the diameter of a circle, its circumference being known; (f) to ascertain the amount to be charged for carriage for a given number of pounds of freight at a certain rate per one hundred pounds; and, further, to solve other problems in which a part bears certain relations to the whole-as, for example, the speed of a railway-train per hour or per minute, knowing the number of miles run per day, or the reverse; or to ascertain the interest on a certain sum of money at a certain rate per cent.; to ascertain the amount to be charged for carrying freight at a given rate per one hundred pounds, 8m.

Referring to the annexed drawings, forming a part of this specification, Figure 1 is a plan of the device by which my invention is carried out. Fig. 2 is a detail view of the movable scale and magnifying-glass. Fig. 3 isa cross section thereof.

A represents the plane of my improved cat culator, and it may be made of wood, metal, paper, or any other suitable material, the ma terial not being of the invention. As shown in the drawings, it is of sheet metal secured to a base of wood by means of screws. In structure it embraces a quadrant of a circle, or an arc of ninety degrees. The left-hand side, or the vertical radius of this are, is shown divided into one hundred equal parts, and the horizontal lines, drawn parallel to the horizontal radius or base, are numbered from 0, beginning with the line next the base, as 10, in a decimal scale, 20, 30, 40, 50, and so on, up to 1,000. As shown, the lines are the one-hundredth part of the height of the perpendicular apart. It will be understood that in practice this perpendicular may be divided into 100, 1,000, 10,000, or any other desired number of equal parts; and then of course a horizontal line must be drawn through each division, making 100, 1,000, 10,000, &c., lines, and then these horizontal lines will be distant from one another the one hundredth, onethousandth, ten thousandth, 850., of the perpendicular. The tens may be indicated, for convenience, in one column,.the hundreds in another. It will be noticed that on the perpendicular, in all numbers between 100 and 200, 200 and 300, 300 and 400, 810., the hundreds figure is omitted. This is simply for convenience; and for the sake of prominence the even hundreds, and, if desired, the fifties, are indicated in a column to the left of the tens, and may for greater prominence be printed or indicated in a different color.

From 9 as a center two arcs, a and b, are drawn at a given distance apart. The former, a, is numbered, as in the vertical, from the base-line upward, from 0 to 99, the hundredth and the uppermost horizontalline coinciding. The are b is numbered in inverse order-that is, beginning at the top and running down to the base-line, which is numbered 100. This are or scale I) is known as the arbitrary scale, and from these two arcs or scales, by aid of the indicator d, hereinafter described, the difference between any given per cent. and

one hundred per cent. will always be shown on the arbitrary scale, making it only necessary in reducing two numbers to a per cent. to find what per cent. one is of the whole, the other per cent. or the accruing per cent. will be shown at once on the arbitrary scale. The horizontal lines extend to the inner are, a, dividing it, as shown, into the same number of parts and of equal extent in perpendicular height as those on the perpendicular. The outer are, I), is divided into the same number of parts as the are a,- but these divisions are of greater extentthan are those on are a, which difference in extent is in proportion to the extent or height of are b, as compared with the height of are a, so that a line drawn from the center 9 of both arcs to a point beyond are I) will out both are a and are I) at the same number of divisions from their baselines. On account of the inverse numbering (valuing of the division) of the are I) the sum of the two divisions thus cut will be one hundred. So with any number on are a, when out by the movable indicator as a radius, (the movable indicator to be described,) its complement of 100 will be shown on are 0, theim'licatorserving, of course, as the radius drawn to a point beyond the outer arcas, for example, as shown in Fig. l, 25 on the inner are, a, on the outer are, Z), their sum 100.

' The divisions 011 the are will be in number one hundred, one thousand, or ten thousand, as the case may be, and will be numbered or sealed to read, when for use of percentages: one hundred divisions, 1, 2, 8, &e., to one thousand divisions, 1, 1 1 1", 2, 2 2 and so 011 to 100; ten thousand divisions, 1 l, &c., to 100, while the lines on the surface, which out also the perpendicular, will be nunr bered for each line, increasing from the base upward, according to the number of lines and to the value given each line. (For example, say the lines are in number one hundred. If each line counts one, the maximum will be one hundred; if two, the maximum will be two hundred; if ten, the maximum will be one thousand &e.)

Thus it will be seen that the drawings illustrate, as has been said, only one of a variety of divisions and markings, being marked on the perpendicular and movable indicator every 10 to 1,000, and on the percentage arcs or scales every 1 to 100; but even with this present arrangement the capacity of the calculator can be doubled, 810., by giving to each horizontal line twice, &c., its valuethat is, one hundred will be two hundred, two hundred will be four hundred, &e.while the percentage scales must, of course, remain the same, their maximum number being one hundred.

The movable indicator (Z, made of any suitable material, is pivoted, as at g, at the right angle of the plane A, and is divided, and the divisions are marked with figures exactly as in the vertical, so that when this indicator is turned upon its pivot till its lei'thand edge lies immediately upon or parallel with the vertical divisions in it, and the numerals marked on it will exactly coincide with and correspond to those on the vertical, and when the indicator is turned to its lowest position its left hand edge (now the upper edge) will fall directly on and coincide with the baseline.

This indicator is provided with a pivot-joint or a tongued-andgroovcd end, fitting a corresponding part on the plane, so as to protect the pivot from dislocation by means of ajar, and, furthermore, this end is pivoted beneath a guide or shield, 71', as further means of protection. It may also be provided with a magnifying-glass, as c, capable of sliding along the indicator by means ot'a tongue-andgroove connection, as shown in Figs. 2 and The magnifier is not essential, but is quite useful in enabling one to see the figures exactly on the arcs or the line at any time lying beneath the indicator. As attached the glass is secured from loss. A pointer, f, is also provided on the movable carriage to designate the figures to be read.

The following will show the manner of using the calculator for the purposes set forth at the beginning: It is to be understood that problems of great variety may be solved besides those herein specified, these being thought to be su'llicient. A skillful mathematician will readily understand the many uses to which this calculator may be adapted. For illustrations problems involving only tolerably round numbers are selected.

(a) To reduce two or more numbers to a percentage: The movable scale represents the total. The cross-lines represent the parts forming this total, and the scale on the are represents the per cent. (This does' not mean the scale 011 the outsidearc, for that is known as the arbitrary scale.) Take the following mileage, say, viz: 200

Total, 800 Glance your eye along the movable scale to 800, (800 being the total.) Then move the scale down until this 800 intersects the two hundredth cross-line, and on the percentageseale you will find the indicator at 25, which means twentylive per cent. Now move the scale up until 800 is intersected by the four hundred and fiftieth cross-line, when the indicator will show 56%. The next, 150: move the indicator down until 800 on the movable scale is intersected by 150 on the cross-lines, and the indicator will show 19%, making total 100%.

(b) For another example, we will suppose these same numbers, or miles, as we called them, allowing the two hundred miles, thirtyone per cent. To know that two hundred is ICC twenty-five per cent. of the whole; but as we allow this line (the two-hundred-mile line or railroad) thirty-one per cent., this thirty-one per cent. is arbitrary, and must be set aside. The balance then is to be prorated on the remaining miles. WVe have now 800 Move the indicator to 31 on the arbitrary scale. Find where the balance miles (via, 600) intersect the movable scale while at this point. This you will find is at 870, (six hundredth cross-line intersects the movable scale at 870.) Now 870 virtually becomes your total, (because the demand of six per cent. more made by the two-hundred-1nile line is equivalent to adding miles to its distance, and thereby increasing the total that amount.) Move the scale down until the four hundred and fiftieth cross-line intersects the movable scale at 870, and on the percentage-scale you have 52%. Now move the scale up until one hundred and fiftieth cross-line intersects 870, and on the percentage-scale you have 17%, which shows as follows, viz:

(c) To divide a number or an amount of money on certain per cents: Take, for ex ample, $7.00 to be divided on 50% ((1) To divide a given numberin the sameproportion that several ditl'erent numbers stand to each other. For example, divide $6.90 between three railroads together earning that amount as charges on freight, on basis of number of miles each handled the freigl1tsay A road, one hundred and fifty miles; 13 road,two hundred miles; 0 road, two hundred and fifty miles; total, siX hundred miles. On the movable scale you find 690, the amount to be divided. Move it up until it intersects 600 on the cross-lines, (six hundred being the total mileage.) Now, in this position, as 600 is to 690, so will any part of (500 show its proportionate part of 690viz:

A road, 150 1. 70

B road, 200 2. 30

0 road, 250 2. 90

In the same way you can ascertain what should accrue to a road four hundred miles longat the same rate per ton per mile. Should the miles exceed in number the amount to be divided, (for instance, 690 and $6.00,) then the position will be reversedthe miles on the movable scale and the amount on the crosslines.

Having thus described my invention, both as to its construction and manner of opera tion,whatI claim asnew, and desire to secure by Letters Patent, is-

1. An improved calculator comprising a plane, in figure a ninety-degree arc graduated along its surface that the projections of these lines forming this graduation mark two scalesone along the arc, numbering from 0 to 100, increasing from the base upward, and the other along the perpendicular, increasing also from the base upward, substantially as described.

2. A plane having two graduated arcs of ninety degrees, numbering one from 0 to 100, from the top downward, the other from 0 to 100, from the bottom upward, and so arranged, one with reference to the other, that a radius drawn to intersect both arcs will cut them at' divisions so numbered that their sum will be 100, substantially as described ,and for the purposes specified.

In combination, a plane, as A, provided with the vertical graduated scale 0 and the two arcs a 1), divided and marked as shown, and the movable indicator d, marked and divided as shown, all for the purposes specified.

4. A calculator comprising a graduated plane, and having two arcs and a vertical line, all divided and marked as shown and described, and a movable indicator having a rule-joint, and a protector, as h, the said indicator being provided with a magnifyingglass and a pointer to indicate more clearly the numbers on the said arcs and the horizontal lines which graduate the plane, as described, and for the purpose specified.

5. A calculator comprising a graduated plane having two arcs inversely marked, a vertical line marked in the same direction as one of the arcs and arising from the center of the two arcs, a graduated movable indicator marked the same as the vertical, and provided with a pivot-joint at the center of said arcs, and a keeper, as h, for the purposes specified.

6. A calculator comprising the plane A, provided with a series of horizontal lines, marked as described, and two arcs, one num- IIO bered from top to bottom, the other from bottom to top, in combination with the glitdllated movable indicator, said indicator being marked and numbered as is the vertical, and being provided with a magnifier and a pointer, whereby said indicator more clearly indicates the desired number on the said arcs or on the horizontal lines which graduate the said plane, substantially as described.

7. The combination of an are numbered from 0 to 100 upward, an are numbered from 0 to 100 downward, a vertical line erected from the point from which the said arcs are drawn and numbered upward from 0 to 1,000, and a movable indicator divided as is the vertical and pivoted at the angle of the said arcs, (or point from which said arcs are drawn) and being marked from 0 to 1,000 from the pivotpoint toward the free end, substantially as described.

In testimony that I claim the foregoing as my own I affix my signature in presence of two witnesses.

METHVEN T. FREEMAN.

\Vitnesscs:

EDWARD E. ELL'Is, O. E. DUFFY. 

